Apparatus and method for demultiplexing a frequency division multiplexed input signal and polyphase digital filter network therefor

ABSTRACT

A filter network demultiplexes a frequency division multiplexed input signal which involves a reduced number of multiplier or multiplying steps. The filter network comprises L−1 Z −N  shift registers in series receiving the multiplexed input signal Y(n) to produce L−1 corresponding shifted signals, pairs of which are added. The filter network further comprises a set of q multiplier sections including p first multiplier sections each being coupled to the added signals for combining each output of a corresponding set of N transformed filter coefficients g i . There are provided a set of N second adder sections each being coupled to distinct outputs of the multiplier sections for producing a corresponding set of N transformed signals, and a set of t third adders each receiving a distinct pair of signals {C T (n),C T′ (n)} from the transformed signals C k (n) for producing a first filtered signal A o (n) and a set of N−1 filtered signals A k (n+k), with k=1, . . . , N−1.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to telecommunication field, and more particularlyto apparatus and method for demultiplexing a frequency divisionmultiplexed signal using a polyphase digital filter network.

2. Description of Prior Art

The use of satellites with multiple spot beam is a major step inincreasing the capabilities of satellite communication. Multiple beamsatellites have the advantage of having high gain and allowing the reuseof the same frequency band in geographically separated beams. The use ofmultiple spot beams requires additional switching on-board thesatellite. This switching can be done either in the RF, IF or thebaseband. Switching at the RF and IF necessitates the use of TimeDivision Multiple Access (TDMA) in the uplink which could lead to highrate modems in the earth stations, therefore increasing the cost ofearth stations. On-board switching in the baseband requiresdown-conversion, demultiplexing and demodulation of the uplink dataprior to switching and remultiplexing, remodulation and upconversionafter switching to form the downlink. The part of the signal processingin the baseband is called On-board Baseband Processing (OBP). The use ofthe OBP results in a considerable flexibility in the choice of theaccess scheme and either TDMA or Frequency Division Multiple Access(FDMA) can be used. For the payloads with OBP, the use of FDMA isconsidered on the uplink to reduce ground station cost. On the otherhand, Time Division Multiplexing (TDM) is used for its power efficiencyon the downlink.

Moreover, use of FDMA on the uplink reduces the size of the earthterminal as compared to TDMA. However, the price paid is the increasedcomplexity of the spacecraft payload. While a single demodulator issufficient for demodulation of high bit rate TDMA on the uplink, severaldemodulators are required for the demodulation of the FDMA carriersreceived by the satellite. A solution to this problem is the use of amulti-carrier demodulator, referred to as a groupdemultiplexer/demodulator. Group demultiplexing is needed, for example,in the digital signal processing payloads if the uplink uses FDMA orsome other type of spectrum sharing such as MF-TDMA or MF-CDMA. The moreimportant and computational intensive section, referred to as the groupdemultiplexer, divides the incoming composite spectrum into separatechannels. The second section, the demodulator, recovers the digital datafor each individual channel.

There are several techniques for the group demultiplexer design. Astraightforward method is per-channel filtering. In this method, aseparate filter is used for each channel. This is only feasible for asmall number of channels. For a large number of channel, sharp filterswith many taps are required. Another method is the FFT/IFFT orfrequency-domain filtering. In this method, a Fast Fourier Transform(FFT) is used to find the frequency spectrum of the composite FDMsignal. Following the FFT, the frequency-domain coefficients aremultiplied by coefficients of a filter in order to determine thefrequency-domain samples falling into each of the carrier channels. Foreach set of frequency-domain coefficients, an Inverse FFT (IFFT) is usedto recover the time-domain samples of the modulated carriers. Thismethod is much less complex than the per-channel approach, while havinga great degree of flexibility.

Another method for the implementation of the group demultiplexer is thepolyphase/FFT method. In this method, a digital filter bank isimplemented in cascade with an DFT processor, and preferably a FFTprocessor to provide better efficiency. This technique can be used whenthe bandwidths of the channels are equal and fixed. FIG. 1 is a blockdiagram of a polyphase/FFT group demultiplexer according to the priorart and generally designated at 10. Input Y(z) at 12, 12′ and outputsX_(k)(z^(N)) at 14, 14′ with k=0, . . . , N−1, are in complex sampledform, as well known in the art, with solid lines 12, 14 representing theIn-phase (or I) and dotted lines 14, 14′ representing theQuadrature-phase (or Q) components of different signals. The notationused for the representation of the signals and delay elements is in theZ-domain. The elements specified by Z^(−k) in FIG. 1 represent a delayof rT, normally implemented using shift registers of length r. That is,if the input to Z^(−k) is a sample of a time signal u(t) at time kT,denoted by u[n], its output will be a sample of the signal u(t) at timenT−kT, denoted by u[n−k], where T is the time duration between twoconsecutive samples. The symbol Y(z) represents the Z-transform of acomposite signal y[n] consisting of N frequency multiplexed signalsrepresented as follows: $\begin{matrix}{{Y(z)} = {\sum\limits_{n = {- \infty}}^{+ \infty}{{y\lbrack n\rbrack}z^{- n}}}} & (1)\end{matrix}$

The outputs X_(i)(z^(N)), i=0,1, . . . , N−1 represent the N individualsignals after demultiplexing. The Z-transform being represented as afunction of Z^(N) rather than z represents a decimation of the outputsby N, i.e., only every Nth sample of x_(i)[n] is retained. This isconsistent with the Nyquist sampling theorem, relating the number ofsamples required for discrete representation of a signal to itsbandwidth. That is, since the bandwidth of each of the N individualchannels is 1/Nth of the total bandwidth occupied by the compositesignal y(t), to represent each of these individual signals, we need onlyto have 1/Nth of the samples required for perfect reconstruction ofy(t).

The digital filter network 15 comprises a filter bank 16 shown in FIG. 1consisting of sub-filters H_(i)(z^(N)), i=0,1, . . . , N−1, designatedat 17, which is derived from a single prototype Finite Impulse Response(FIR) filter, H(z), through a decimation by N. That is, each sub-filterH_(i)(Z^(N)) consists of 1/Nth of the coefficients of H(z). Denoting thecoefficients of the prototype filter by h_(i), i=0,1, . . . , NL−1, thecoefficients of the sub-filter, H₀(z^(N)), are h₀, h_(N), h_(2N), . . ., h_(N(L−)1), and the coefficients of the sub-filter, H₁(z^(N)), are h₁,h_(N+1), h_(2N+1), . . . , h_(N(L−1)+1). In general, the coefficients ofthe ith sub-filter, H_(i)(z^(N)), are h_(i), h_(N+i), h_(2N+i), . . . ,h_(N(L−1)+i). The derivation of the sub-filters from the prototypefilter is based on the following factorization: $\begin{matrix}{{H(z)} = {{\sum\limits_{n = 0}^{{NL} - 1}{h_{n}z^{- n}}} = {{\sum\limits_{i = 0}^{N - 1}{z^{- i}{\sum\limits_{k = 0}^{L - 1}{h_{{kN} + i}z^{- {kN}}}}}} = {\sum\limits_{i = 0}^{N - 1}{z^{- i}{{H_{i}( z^{N} )}.}}}}}} & (2)\end{matrix}$

The switches 18, 18′ at the input of the sub-filters 17 close every Nsamples connecting the outputs of the shift registers 20 to differentsub-filters. That is, each sub-filter operates at a rate which is 1/Nththat of the sample rate of the input signal, y[n]. Multiplication ofoutput signals A_(i)(n) by w^(i), i=0,1, . . . , N−1 generated atoutputs 19, 19′, where w=e^(−iπ/N) is performed by a set of Nmultipliers 22 and results in a phase shift of iπ/N to produce filteredoutput signals A*_(i)(n) at outputs 21, 21′, from which the FFTprocessor 23 finds the Discrete Fourier Transform (DFT) as defined by:$\begin{matrix}{B_{k} = {\sum\limits_{i = 0}^{N - 1}{A_{i}^{j\frac{2\pi}{N}{ik}}}}} & (3)\end{matrix}$

Finally, the alternate samples of each of the N outputs 25, 25′ of theFFT processor are inverted by the multipliers 24 to producedemultiplexed output signals X_(k)(Z^(N)) at outputs 14, 14′.

From the foregoing, it can be seen that the number of multipliersrequired for the implementation of the polyphase filter network is NL,which correspond to coefficients h₀, h₁, h₂, . . . , h_(NL−1) of theprototype filter. Such a number of multipliers may represents a limitingfactor in the context of payload optimization especially where a highnumber of channels is to be handled by a satellite On-boarddemultiplexer.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide apparatusand method for demultiplexing a frequency division multiplexed inputsignal which involves a reduced number of multipliers or multiplyingsteps.

According to the above object, from a broad aspect of the presentinvention, there is provided a polyphase digital filter network based ona linear phase prototype filter for use in a group demultiplexer forgenerating N output data signals associated with N channels from acorresponding Frequency Division Multiplexed input signal Y(n), saidlinear phase prototype filter comprising N sub-filters beingcharacterized by L coefficients forming NL coefficients for saidprototype filter. The polyphase digital filter network comprises L−1Z^(−N) shift registers in series receiving the multiplexed input signalY(n) to produce L−1 corresponding shifted signals Y(n−rN), with r=1, . .. , L−1, and a set of p first adder sections each receiving a distinctpair of signals from the multiplexed input signal Y(n) and the shiftedsignals Y(n−rN). The filter network further comprises a set of qmultiplier sections including p first multiplier sections each beingcoupled to a respective output of a corresponding one of the first addersections for combining each said output with a corresponding set of Ntransformed filter coefficients g_(i) derived from the coefficients ofthe linear phase prototype filter, the set of q multiplier sectionsincluding a further multiplier section receiving shifted signal$Y( {n - {( \frac{L - 1}{2} )N}} )$

where L is odd for combining thereof in parallel with a correspondingset of s further transformed filter coefficients g_(i) derived from thecoefficients of the linear phase prototype filter. The filter networkfurther comprises a set of N second adder sections each being coupled todistinct outputs of the multiplier sections for producing acorresponding set of N transformed signals C_(k)(n), with k=0, . . . ,N−1; and a set of t third adders each receiving a distinct pair ofsignals {C_(T)(n),C_(T′)(n)} from the transformed signals C_(k)(n) forproducing a first filtered signal A₀(n) and a set of N−1 filteredsignals A_(k)(n+k), with k=1, . . . , N−1.

According to a further broad aspect of the present invention, there isprovided a polyphase/DFT digital group demultiplexer for generating Noutput data signals associated with N channels from a correspondingFrequency Division Multiplexed input signal Y(n), comprising a polyphasedigital filter network based on a linear phase prototype filter formedby N sub-filters being characterized by L coefficients forming NLcoefficients for said prototype filter. The polyphase digital filternetwork comprises L−1 Z^(−N) shift registers in series receiving themultiplexed input signal Y(n) to produce L−1 corresponding shiftedsignals Y(n−rN), with r=1, . . . , L−1; and a set of p first addersections each receiving a distinct pair of signals from the multiplexedinput signal Y(n) and the shifted signals Y(n−rN). The filter networkfurther comprises a set of q multiplier sections including p firstmultiplier sections each being coupled to a respective output of acorresponding one of the first adder sections for combining each saidoutput with a corresponding set of N transformed filter coefficientsg_(i) derived from the coefficients of the linear phase prototypefilter, the set of q multiplier sections including a further multipliersection receiving shifted signal$Y( {n - {( \frac{L - 1}{2} )N}} )$

where L is odd for combining thereof with a corresponding set of sfurther transformed filter coefficients g_(i) derived from thecoefficients of said linear phase prototype filter. The filter networkfurther comprises a set of N second adder sections each being coupled toselected outputs of the multiplier sections for producing acorresponding set of N transformed signals C_(k), with k=0, . . . , N−1;and a set of t third adders each receiving a distinct pair of signals{C_(T)(n),C_(T′)(n)} from the transformed signals C_(k)(n) for producinga first filtered signal A₀(n) and a set of N−1 filtered signalsA_(k)(n+k), with k=1, . . . , N−1. The filter network further comprisesa set of N−1 shift registers Z^(−k) receiving said. filtered signalsA_(k)(n+k) to produce N−1 corresponding filtered signals A_(k)(n), withk=1, . . . , N−1. The group demultiplexer further comprises a set of Nphase offset multipliers receiving the filtered signals A₀(n) andA_(k)(n) forming a set of filtered signals A_(k)(n), with k=0, . . . ,N−1, for combining thereof with a corresponding set of N phase offsetparameter w_(k), with k=0, . . . , N−1, to produce a corresponding setof phase offset filtered signals A*_(k)(n); Discrete Fourier Transformprocessor means for generating a set of N processed output signalsB_(k)(n) from said corresponding set of phase offset filtered signalsA*_(k)(n), with k=0, . . . , N−1; and a set of N output alternateinverting multipliers each receiving a corresponding one of the set ofprocessed output signals B_(k)(n) to generate the N output data signalsassociated with the N channels.

According to a still further broad aspect of the present invention,there is provided a method of demultiplexing a Frequency DivisionMultiplexed input signal Y(n) for generating N output data signalsassociated with N channels, the method comprising the steps of: i)generating L−1 shifted signals Y(n−rN), with r=1, (l−1)N, from themultiplexed input signal Y(n); ii) coupling p pairs of distinct signalsfrom the multiplexed input signal Y(n) and the shifted signals Y(n−rN)to produce p corresponding pairs of coupled output signals; iii)combining each said pair of output signals with a corresponding set of Ntransformed filter coefficients derived from coefficients of a linearphase prototype filter; iv) combining shifted signal$Y( {n - {( \frac{L - 1}{2} )N}} )$

with a corresponding set of s further transformed filter coefficientsderived from the coefficients of the linear phase prototype filter,whenever L is odd; v) coupling the results of the combining steps toproduce N transformed signals C_(k), with k=0, . . . , N−1; vi) couplingdistinct pair of signals {C_(T)(n),C_(T′)(n)} from the transformedsignals C_(k)(n) for producing a first filtered signal A₀(n) and a setof N−1 filtered signals A_(k)(n+k), with k=1, . . . , N−1; vii) shiftingthe filtered signals A_(k)(n+k) to produce N−1 corresponding filteredsignals A_(k)(n), with k=1, . . . , N-−1; viii) phase offsetting thefiltered signals A₀(n) and A_(k)(n) forming a set of filtered signalsA_(k)(n), to produce a corresponding set of phase offset filteredsignals A*_(k)(n); ix) applying a Discrete Fourier Transform on thephase offset filtered signals A*_(k)(n) to generate a set of N outputsignals B_(k)(n), with k=0, . . . , N−1; and x) alternately invertingthe output signals B_(k)(n) to generate the N output data signalsassociated with the N channels.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a polyphase/FFT group demultiplexeraccording to the prior art;

FIG. 2 is a block diagram of a typical digital filter network based on alinear phase prototype filter according to the prior art;

FIG. 3 is a general block diagram of a polyphase/FFT group demultiplexeraccording to a preferred embodiment of the present invention;

FIG. 4 is a block diagram of a first example of a digital polyphasenetwork according to the preferred embodiment of the present invention,where the number N of channels and the number L of coefficients persub-filter are both even;

FIG. 5 is a block diagram of a variant of the example shown in FIG. 4,which provides a time-multiplexed output;

FIG. 6 is a block diagram of a second example of a digital polyphasenetwork according to the preferred embodiment of the present invention,where the number N of channels is odd and the number L of coefficientsper sub-filter is even;

FIG. 7 is a block diagram of a third example of a digital polyphasenetwork according to the preferred embodiment of the present invention,where the number N of channels and the number L of coefficients persub-filter are both odd;

FIG. 8 is block diagram of a fourth example of a digital polyphasenetwork according to the preferred embodiment of the present invention,where the number N of channels is even and the number L of coefficientsper sub-filter is odd.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention takes advantage of the symmetry found in linearphase prototype filter in order to reduce the number of the requiredmultipliers or multiplying steps up to one half of that normally used.While taking advantage of the symmetry may be straightforward for theimplementation of a single filter, as it can be seen for each sub-filterof the prototype filter forming the digital filter network 30 shown inFIG. 2, which prototype filter is characterized by symmetriccoefficients, i.e., h₀=h_(NL−1), h₁=h_(NL−2) or, in general,h_(i)=h_(NL−1−i), i=0, . . . , NL−1, with N=4 and L=6 (NL=24) in theexample shown, that it is not the case for a polyphase filter network,since symmetrically located multipliers operate on different samples ofthe input. In the case of a single output filter, one simply needs toadd the input samples to be multiplied by the same coefficients beforemultiplication and, therefore, performs one multiplication instead oftwo. In the case of polyphase filter bank, since the multipliers withsimilar coefficients do not contribute to the same output, the simpletechnique of adding symmetrically opposed samples does not work. It ispointed out that the shift registers 31 in the filter branches are shownas function of Z instead of z in order to emphasize the fact that theseshift registers are clocked at one fourth the input sample rate. As aresult, each single shift through these delay elements is equivalent toa delay of 4T, T being the period associated with the sampling rate.

Referring now to FIG. 3, there is shown a polyphase/FFT groupdemultiplexer according to a preferred embodiment of the presentinvention and generally designated at 32, which comprises a polyphasefilter network 34 being based on a linear phase prototype filter andreceiving a Frequency Division Multiplexed input signal Y(Z) in complexsampled form at 12, 12′. The demultiplexer 32 further comprises a firstset of N multipliers 22 for applying a phase shift of iπ/N to thefiltered output signals A_(i)(n) as generated at outputs 19, 19′ of thefilter network 34, followed by a FFT processor 23 for applying aDiscrete Fourier Transform (DFT) to the filtered output signals A_(i)(n)as obtained at outputs 21, 21′ of multipliers 22. Finally, a second setN multipliers 24 are provided for inverting alternate samples of each ofthe N output signals of the FFT processor 23 as generated at outputs 25,25′ to produce demultiplexed output signals X_(k)(Z^(N)) at outputs 14,14′ in complex sampled form. It should be pointed out that apart fromthe filter network 34, a same system architecture as found in the priorart is employed in the design of the demultiplexer shown in FIG. 3,generating same output signals A_(i)(n), A_(i)(n) and X_(k)(Z^(N)), butwith higher efficiency due to a reduced number of multipliers as part ofthe filter network 34, as will be later explained in more detail. In thefollowing FIGS. 4 to 8, all signals are in complex form having anIn-phase (I) and a Quadrature-phase (Q) component, as explained before.However, for the sake of clarity, single lines instead of pairs of solidand dotted lines are illustrated.

Referring to FIG. 4, a polyphase digital filter network for use as partof a group demultiplexer as generally described above and in accordanceto the present invention will be now described for a first particularexample wherein N and L are both even, using a four (N=4) channelpolyphase digital network 34 based on a prototype filter such as shownin FIG. 2 (L=6). However, since the present invention is applicablewhenever N or L are chosen to be either even or odd integers, thefollowing mathematical expressions cover all possible combinations ofinteger: values for N and L, as it will be later explained in moredetail with reference to FIGS. 6 to 8. As shown in FIG. 4, the filternetwork 34 comprises L−1 Z^(−N) shift registers 36 in series receivingthe multiplexed input signal Y(n) via an input line 38, to produce L−1corresponding shifted signals Y(n−rN), with r=1, . . . , L−1 throughoutput lines 40 forming filter branches. The filter network 34 furthercomprises a set of p first adder sections 42 as delimited with dottedlines in FIG. 4, each receiving through corresponding ones of lines 40 adistinct pair of signals {Y(n−mN),Y(n−(L−(1+m)N))} from the multiplexedinput signal Y(n) and the shifted signals Y(n−rN), wherein:$\begin{matrix}{p = \{ {\begin{matrix}\frac{L}{2} & {{where}\quad L\quad {is}\quad {even}} \\\frac{L - 1}{2} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};\quad {and}} } & (4) \\{m = \{ {\begin{matrix}{0,\ldots \quad,\frac{L - 2}{2}} & {{where}\quad L\quad {is}\quad {even}} \\{0,\ldots \quad,\frac{L - 3}{2}} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} } & (5)\end{matrix}$

and therefore p=3 and m=2 in the present example. Each first addersection 42 includes a first adder 44 having a pair of positive inputs 45receiving the distinct pair of signals {Y(n−mN),Y(n−(L−(1+m)N))} and anoutput line 46, and a second adder 48 having positive and invertinginputs 49, 49′ receiving also the signals {Y(n−mN),Y(n−(L−(1+m)N))}respectively, and an output line 50. Each pair of first and second adderoutput lines 46 and 50 form a respective output for the correspondingfirst adder section 42. The filter network 34 further comprises a set ofq multiplier sections including p first multiplier sections 52 asdelimited with dotted lines in FIG. 4, each being coupled to arespective output of a corresponding one of the first adder sections 42for combining each output with a corresponding set of N transformedfilter coefficients g_(i) derived from the coefficients of the linearphase prototype filter, wherein: $\begin{matrix}{q = \{ {\begin{matrix}p & {{where}\quad L\quad {is}\quad {even}} \\{p + 1} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} } & (6)\end{matrix}$

and therefore q=p=4 in the present example. The method of obtainingvalues for g_(i) will be explained later in more detail. As will bedescribed later with reference to FIGS. 7 and 8 where L is odd, in thatcase the set of q multiplier sections includes a further multipliersection receiving shifted signal$Y( {n - {( \frac{L - 1}{2} )N}} )$

for combining thereof in parallel with a corresponding set of s furthertransformed filter coefficients g_(i) derived from the coefficients ofthe linear phase prototype filter, wherein: $\begin{matrix}{s = \{ \begin{matrix}\frac{N}{2} & {{where}\quad N\quad {is}\quad {even}} \\\frac{N + 1}{2} & {{{where}\quad N\quad {is}\quad {odd}};}\end{matrix} } & (7)\end{matrix}$

therefore s=0 in the present example since L is even. Each firstmultiplier section 42 comprises N multipliers 54 each having arespective output M_(i) 56 and being coupled in parallel to thecorresponding first adder output for combining thereof with Ncorresponding transformed filter coefficients g_(i), and s multiplierseach having an output M_(i) and being coupled in parallel to thecorresponding second adder section output for combining thereof with thecorresponding further transformed filter coefficients g_(i). The filternetwork 34 is further provided with a set of N second adder sections 58as delimited with dotted lines in FIG. 4, each being coupled to distinctoutputs 56 of the multiplier sections 52 for producing a correspondingset of N transformed signals C_(k)(n) with k=0, . . . , N−1, throughoutput lines 60, according to the following equation: $\begin{matrix}{{{C_{k}(n)} = {\sum\limits_{i = {k + {Nl}}}M_{i}}};{{with}\quad \{ \begin{matrix}{{l = 0},\ldots \quad,{\frac{L}{2} - 1}} & {{where}\quad L\quad {is}\quad {even}} \\{{l = 0},\ldots \quad,\frac{L - 1}{2}} & \begin{matrix}{{where}\quad L\quad {is}\quad {odd}} \\{{and}\quad k\quad {is}\quad {even}}\end{matrix} \\{{l = 0},\ldots \quad,\frac{L - 3}{2}} & \begin{matrix}{{where}\quad L\quad {is}\quad {odd}} \\{{and}\quad k\quad {is}\quad {{odd}.}}\end{matrix}\end{matrix} }} & (8)\end{matrix}$

There is further provided a set of t third adders 59 each receiving adistinct pair of signals {C_(T)(n),C_(T′)(n)} from the transformedsignals C_(k)(n) for producing through output lines 61, a first filteredsignal A₀(n) and a set of N−1 filtered signals A_(k)(n+k), with k=1, . .. , N−1, wherein: $\begin{matrix}{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2u}(n)},{C_{{2u} + 1}(n)}} \} \{ \begin{matrix}{{{{for}\quad u} = 0},\ldots \quad,{\frac{N}{2} - 1}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = 0},\ldots \quad,\frac{N - 3}{2}} & {{{where}\quad N\quad {is}\quad {odd}};}\end{matrix} }} & (9) \\{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2{({n - u - 1})}}(n)},{- {C_{{2{({n - u})}} - 1}(n)}}} \} \{ \begin{matrix}{{{{for}\quad u} = \frac{N}{2}},\ldots \quad,{N - 1}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = \frac{N + 1}{2}},\ldots \quad,{N - 1}} & {{{where}\quad N\quad {is}\quad {odd}};}\end{matrix} }} & (10) \\{t = \{ \begin{matrix}N & {{where}\quad N\quad {is}\quad {even}} \\{N - 1} & {{{where}\quad N\quad {is}\quad {odd}};{and}}\end{matrix} } & (11) \\{{A_{u = \frac{N - 1}{2}}( {n + \frac{N - 1}{2}} )} = {{C_{N - 1}(n)}\quad {where}\quad N\quad {is}\quad {{odd}.}}} & (12)\end{matrix}$

According to a parallel output implementation used in the present firstexample, the filter network further comprises N−1 Z^(−k) shift registers62 receiving the filtered signals A_(k)(n+k) to produce N−1corresponding filtered signals A_(k)(n), with k=1, . . . , N−1., whichare fed to the multipliers 22 as explained before with reference to FIG.3. Thus, this implementation generates four parallel output samplesevery four clock cycles. That is, for each four sample of y[n], there isone set of four output samples available every fourth outputs by T, 2T,3T, respectively, so that all four output samples are availablesimultaneously every four clock cycles.

Referring now to FIG. 5, a block diagram of a variant of the polyphasedigital filter network according to the first example shown in FIG. 4 isshown, which provides a time-multiplexed output. That implementationonly differs from the parallel output implementation in that it isadapted to work with a commutation device 64 and in that no output shiftregisters are provided, for directly generating A_(k)(n), with k=1, . .. , N−1., serially in a time multiplexed format. Comparing the prior artfilter network shown in FIG. 2 with the filter network of the exampleshown in FIG. 4, it is interesting to note that the reduction in thenumber of multipliers, estimated as $\frac{NL}{2}$

where L is even, is not achieved at the expense of an. increase in thenumber of shift registers or adders. In fact, the number of adders iseven reduced, while the number of shift registers remain unchanged. Asto the variant shown in FIG. 5, the number of shift registers has beenfurther reduced by N−1.

The basic scheme inherent to a polyphase digital filter network for useas part of a group demultiplexer as generally described above and inaccordance to the present invention will be now developed for the firstexample shown in FIG. 4, using the relations set out above. Theexpressions for A₀[n], A₁[n], A₂[n] and A₃[n] can be expressed asfollows:

A ₀ [n]=h ₀ y[n]+h ₄ y[n−4]+h ₈ y[n−8]+h ₁₁ y[n−12]+h ₇ y[n−16]+h ₃y[n−20]  (13.1)

A ₁ [n]=h ₁ y[n−1]+h ₅ y[n−5]+h ₉ y[n−9]+h ₁₀ y[n−13]+h ₆ y[n−17]+h ₂y[n−21]  (13.2)

A ₂ [n]=h ₂ y[n−2]+h ₆ y[n−6]+h ₁₀ y[n−10]+h ₉ y[n−14]+h ₅ y[n−18]+h ₁y[n−22]  (13.3)

A ₃ [n]=h ₃ y[n−3]+h ₇ y[n−7]+h ₁₁ y[n−11]+h ₈ y[n−15]+h ₄ y[n−19]+h ₀y[n−23]  (13.4)

Substituting n+1, n+2 and n+3 in (13.1), (13.2) and (13.3), gives:

A ₀ [n]=h ₀ y[n]+h ₄ y[n−4]+h ₈ y[n−8]+h ₁₁ y[n−12]+h ₇ y[n−16]+h ₃y[n−20]  (14.1)

A ₁ [n+1]=h ₁ y[n]+h ₅ y[n−4]+h ₉ y[n−8]+h ₁₀ y[n−12]+h ₆ y[n−16]+h ₂y[n−20]  (14.2)

A ₂ [n+2]=h ₂ y[n]+h ₆ y[n−4]+h ₁₀ y[n−8]+h ₉ y[n−12]+h ₅ y[n−16]+h ₁y[n−20]  (14.3)

A ₃ [n+3]=h ₃ y[n]+h ₇ y[n−4]+h ₁₁ y[n−8]+h ₈ y[n−12]+h ₄ y[n−16]+h ₀y[n−20]  (14.4)

Let's define the auxiliary variables C₀[n], C₁[n], C₂[n] and C₃[n] asfollows: $\begin{matrix}{{{C_{0}\lbrack n\rbrack} = \frac{{A_{0}\lbrack n\rbrack} + {A_{3}\lbrack {n + 3} \rbrack}}{2}};} & (15.1) \\{{{C_{1}\lbrack n\rbrack} = \frac{{A_{0}\lbrack n\rbrack} - {A_{3}\lbrack {n + 3} \rbrack}}{2}};} & (15.2) \\{{{C_{2}\lbrack n\rbrack} = \frac{{A_{1}\lbrack {n + 1} \rbrack} + {A_{2}\lbrack {n + 2} \rbrack}}{2}};} & (15.3) \\{{{C_{3}\lbrack n\rbrack} = \frac{{A_{1}\lbrack {n + 1} \rbrack} - {A_{2}\lbrack {n + 2} \rbrack}}{2}};} & (15.4)\end{matrix}$

Substituting for A₀[n], A₁[n+1], A₂[n+2] and A₃[n+3] from equations(14.1) to (14.4) and using coefficients g_(i), i=0, . . . , 11 given inTable 1, gives:

TABLE 1 g₀ (h₀ + h₃)/2 g₁ (h₀ + h₃)/2 g₂ (h₁ + h₂)/2 g₃ (h₁ − h₂)/2 g₄(h₄ + h₇)/2 g₅ (h₄ − h₇)/2 g₆ (h₅ + h₆)/2 g₇ (h₅ − h₆)/2 g₈ (h₈ + h₁₁)/2g₉ (h₈ − h₁₁)/2 g₁₀ (h₉ + h₁₀)/2 g₁₁ (h₉ − h₁₀)/2

 C ₀ [n]=g ₀ {y[n]+y[n−20]}+g ₄ {y[n−4]+y[n−16]}+g ₈{y[n−8]+y[n−12]}  (16.1)

C ₁ [n]=g ₁ {y[n]−y[n−20]}+g ₅ {y[n−4]−y[n−16]}+g ₉{y[n−8]−y[n−12]}  (16.2)

C ₂ [n]=g ₂ {y[n]+y[n−20]}+g ₆ {y[n−4]+y[n−16]}+g ₁₀{y[n−8]+y[n−12]}  (16.3)

C ₃ [n]=g ₃ {y[n]−y[n−20]}+g ₇ {y[n−4]−y[n−16]}+g ₁₁{y[n−8]−y[n−12]}  (16.4)

Comparing equations and (14) and (16), it is observed that whilecomputation of A_(i)[n], i=0, 1, 2, 3 requires 24 multiplying steps,computation of C_(i)[n], i=1, 2, 3 needs only $\frac{NL}{2} = 12$

multiplying steps. Therefore, it is more efficient to compute C_(i)[n]'sfirst and then calculate A₀[n], A₁[n+1], A_(2[n+)2], A_(3[n+)3] usingthe following equations and, finally, find A_(i)[n]'s by shifting thesedelayed outputs:

A ₀ [n]=C ₀ [n]+C ₁ [n];  (17.1)

A ₁ [n+1]=C ₂ [n]+C ₃ [n];  (17.2)

A ₂ [n+2]=C ₂ [n]−C ₃ [n];  (17.3)

A ₃ [n+3]=C ₀ [n]−C ₁ [n];  (17.4)

Now, the derivation for the general case of any even integer values forN and L will be presented. Denoting the outputs of the filter network byA₀[n], A₁[n], . . . , A_(N−1)[n], we have:

A ₀ [n]=h ₀ y[n]+h _(N) y[n−N]+ . . . +h _((L−1)N) y[n−(L−1)N]  (18.1)

A ₁ [n]=h ₁ y[n−1]+h _(N+1) y[n−(N+1)]+ . . . +h _((L−1)N+1)y[n−(L−1)N−1]  (18.2)

A ₂ [n]=h ₂ y[n−2]+h _(N+2) y[n−(N+2)]+ . . . +h _((L−1)N+2)y[n−(L−1)N−2]  (18.3)

A _(N−1) [n]=h _(N−1) y[n−(N−1)]+h _(2N−1) y[n−(2N−1)]+ . . . +h _(LN−1)y[n−(LN−1)]  (18.N)

Taking advantage of the symmetry of the coefficients of the linear phasefilter, i.e., h_(k)=h_((NL−1)−k) for k=0, . . . , LN−1 gives:

A ₀ [n]=h ₀ y[n]+h _(N) y[n−N]+ . . . +h _(N−1) y[n−(L−1)N]  (19.1)

A ₁ [n]=h ₁ y[n−1]+h _(N+1) y[n−(N+1)]+ . . . +h _(N−2)y[n−(L−1)N−1]  (19.2)

A ₂ [n]=h ₂ y[n−2]+h _(N+2) y[n−(N+2)]+ . . . +h _(N−3)y[n−(L−1)N−2]  (19.3)

A _(N−1) [n]=h _(N−1) y[n−(N−1)]+h _(2N−1) y[n−(2N−1)]+ . . . +h ₀y[n−(LN−1)]  (19.4)

Substituting n+1, n+2, . . . , n+(N−1) for n in the 1st., 2nd., . . . ,Nth. equation, gives the following equations:

A ₀ [n]=h ₀ y[n]+h _(N) y[n−N]+ . . . +h _(N−1) y[n−(L−1)N]  (20.1)

 A ₁ [n+1]=h ₁ y[n]+h _(N+1) y[n−N]+ . . . +h _(N−2) y[n−(L−1)N]  (20.2)

A ₂ [n+2]=h ₂ y[n]+h _(N+2) y[n−N]+ . . . +h _(N−3) y[n−(L−1)N]  (20.3)

A _(N−1) [n+N−1]=h _(N−1) y[n]+h _(2N−1) y[n−N]+ . . . +h ₀y[n−(L−1)N]  (20.N)

These equations are the generalization of the equations (14.1) to(14.4). Then, let's define the following auxiliary variables as follows:$\begin{matrix}{{C_{0}\lbrack n\rbrack} = \frac{{A_{0}\lbrack n\rbrack} + {A_{N - 1}\lbrack {n + N - 1} \rbrack}}{2}} & (21.1) \\{{C_{1}\lbrack n\rbrack} = \frac{{A_{0}\lbrack n\rbrack} - {A_{N - 1}\lbrack {n + N - 1} \rbrack}}{2}} & (21.2) \\{{C_{2}\lbrack n\rbrack} = \frac{{A_{1}\lbrack {n + 1} \rbrack} + {A_{N - 2}\lbrack {n + N - 2} \rbrack}}{2}} & (21.3) \\{{{C_{3}\lbrack n\rbrack} = \frac{{A_{1}\lbrack {n + 1} \rbrack} - {A_{N - 2}\lbrack {n + N - 2} \rbrack}}{2}}\quad \vdots} & (21.4) \\{{C_{N - 2}\lbrack n\rbrack} = \frac{{A_{\frac{N}{2} - 1}\lbrack {n + \frac{N}{2} - 1} \rbrack} + {A_{\frac{N}{2}}\lbrack {n + \frac{N}{2}} \rbrack}}{2}} & ( {{21.N} - 1} ) \\{{C_{N - 1}\lbrack n\rbrack} = \frac{{A_{\frac{N}{2} - 1}\lbrack {n + \frac{N}{2} - 1} \rbrack} - {A_{\frac{N}{2}}\lbrack {n + \frac{N}{2}} \rbrack}}{2}} & ( {21.N} )\end{matrix}$

These equation are the generalization of the equations (15.1) to (15.4).Thus, the auxiliary variables can be expressed as follows:

C ₀ [n]=g ₀ {y[n]+y[n−(L−1)N]}+g _(N) {y[n−N]+y[n−(L−2)N]}+ . . . +g_((L/2−1)N) {y[n−(L/2−1)N]+y[n−L/2N]}  (22.1)

C ₁ [n]=g ₁ {y[n]−y[n−(L−1)N]}+g _(N+1) {y[n−N]−y[n−(L−2)N]}+ . . . +g_((L/2−1)N+1) {y[n−(L/2−1)N]−y[n−L/2N]}  (22.2)

C ₂ [n]=g ₂ {y[n]+y[n−(L−1)N]}+g _(N+2) {y[n−N]+y[n−(L−2)N]}+ . . . +g_((L/2−1)N+2) {y[n−(L/2−1)N]+y[n−L/2N]}  (22.3)

C _(N−1) [n]=g _(N−1) {y[n]−y[n−(L−1)N]}+g _(2N−1) {y[n−N]−y[n−(L−2)N]}+. . . +g _(L/2N−1) {y[n−(L/2−1)N]−y[n−L/2N]},  (22.N)

wherein: $\begin{matrix}{g_{0} = \frac{h_{0} + h_{N - 1}}{2}} \\{g_{1} = \frac{h_{0} - h_{N - 1}}{2}} \\{g_{2} = \frac{h_{1} + h_{N - 2}}{2}} \\{g_{3} = \frac{h_{1} - h_{N - 2}}{2}} \\\vdots\end{matrix}$

and in general: $g_{i} = \frac{h_{j} + h_{k}}{2}$

for i even; and $g_{i} = \frac{h_{j} \mp h_{k}}{2}$

for i odd

wherein${j = {{\lbrack \frac{i}{N} \rbrack \quad \frac{N}{2}} + \lbrack \frac{i}{2} \rbrack}};\quad {and}$$k = {{( {{3\lbrack \frac{i}{N} \rbrack} + 2} )\frac{N}{2}} - \lbrack \frac{i}{2} \rbrack - 1}$

[x] denoting the largest integer smaller than x.

In the general case where N and L are arbitrary even integers, thenumber of multipliers is reduced from NL to NL/2 and the number ofadditions is reduced from N(L−1) to L(N/2+1).

Referring now to FIG. 6, a second example of a digital polyphase networkaccording to the preferred embodiment of the present invention will bedescribed, which network 34 is characterized by an odd number N=3 ofchannels and an even number L=6 of coefficients per sub-filter. Applyingequation (8) above, and using coefficients g_(i), i=0, . . . , 8 asgiven in Table 2, the set of N=3 transformed signals C_(k)(n), withk=0,1,2, is given by:

C ₀ [n]=g ₀ {y[n]+y[n−15]}+g ₃ {y[n−3]+y[n−12]}+g ₆{y[n−6]+y[n−9]}  (23.1)

C ₁ [n]=g ₁ {y[n]−y[n−15]}+g ₄ {y[n−3]−y[n−12]}+g ₇{y[n−6]−y[n−9]}  (23.2)

C ₂ [n]=g ₂ {y[n]+y[n−15]}+g ₅ {y[n−3]+y[n−12]}+g ₈{y[n−6]+y[n−9]}  (23.3)

TABLE 2 g₀ (h₀ + h₂)/2 g₁ (h₀ − h₂)/2 g₂ h₁ g₃ (h₃ + h₅)/2 g₄ (h₃ −h₅)/2 g₅ h₄ g₆ (h₆ + h₈)/2 g₇ (h₆ − h₈)/2 g₈ h₇

It can be seen from FIG. 6 that the number q of multiplier sections 52,is equal to the number of first adder sections 42, i.e. p=L/2=6/2=3,since L=6 is even, according to equations (4) and (6) above, and that aset of N=3 transformed signals C_(k)(n), with k=0, . . . , 2, isgenerated through output lines 60. It can also be seen that while thereare N=3 second adder sections 58, there are t=N−1=2 third adders 59since N=3 is odd, according to equation (11) above. Therefore,C₂(n)=A₁(n+1) since N=3 id odd, in accordance to equation (12) above.

Turning now to FIG. 7, a third example of a digital polyphase networkaccording to the preferred embodiment of the present invention will benow described, which network 34 is characterized by an odd number N=3 ofchannels and an odd number L=5 of coefficients per sub-filter. Applyingequation (8) above, and using coefficients g_(i), i=0, . . . , 7 asgiven in Table 3, the set of N=3 transformed signals C_(k)(n), withk=0,1,2, is given by:

C ₀ [n]=g ₀ {y[n]+y[n−12]}+g ₃ {y[n−3]+y[n−9]}+g ₆ y[n−6]  (24.1)

C ₁ [n]=g ₁ {y[n]−y[n−12]}+g ₄ {y[n−3]−y[n−9]}  (24.2)

C ₂ [n]=g ₂ {y[n]+y[n−12]}+g ₅ {y[n−3]+y[n−9]}+g ₇ y[n−6]  (24.3)

TABLE 3 g₀ (h₀ + h₂)/2 g₁ (h₀ − h₂)/2 g₂ h₁ g₃ (h₃ + h₅)/2 g₄ (h₃ −h₅)/2 g₅ h₄ g₆ h₆ g₇ h₇

It can be seen from FIG. 7 that the number q of multiplier sections 52,52′ is equal to ${{p + 1} = {{\frac{L - 1}{2} + 1} = {{2 + 1} = 3}}},$

since L=5 is odd, according to equations (4) and (6) above, and that aset of N=3 transformed signals C_(k)(n), with k=0,. . . , 2, isgenerated through output lines 60. According to equation (7) above, thefurther multiplier: section 52′ comprises a number$s = {\frac{N + 1}{2} = {\frac{3 + 1}{2} = 2}}$

of multipliers 54′ receiving the shifted signal${Y( {n - {( \frac{L - 1}{2} )N}} )} = {{Y( {n - {( \frac{5 - 1}{2} )3}} )} = {Y( {n - 6} )}}$

for combining thereof in parallel with a corresponding set of s=2further transformed filter coefficients g_(6 and g) ₇ derived from thecoefficients of the linear phase prototype filter, as shown in Table 3.As for the example shown in FIG. 6, it can also be seen in the exampleof FIG. 7 that while there are N=3 second adder sections 58, there aret=N−1=2 third adders 59 since N=3 is odd, according to equation (11)above. Here again, C₂(n)=A₁(n+1) since N=3 id odd, in accordance toequation (12) above.

Turning now to FIG. 8, a fourth example of a digital polyphase networkaccording to the preferred embodiment of the present invention will benow described, which network 34 is characterized by an even number N=4of channels and an odd number L=5 of coefficients per sub-filter.Applying again equation (8) above, and using coefficients g_(i), i=0, .. . , 9 as given in Table 4, the set of N=4 transformed signalsC_(k)(n), with k=0,1,2,3, is given by:

C ₀ [n]=g ₀ {y[n]+y[n−16]}+g ₄ {y[n−4]+y[n−12]}+g ₈ y[n−8]  (25.1)

C ₁ [n]=g ₁ {y[n]−y[n−16]}+g ₅ {y[n−4]−y[n−12]}  (25.2)

C ₂ [n]=g ₂ {y[n]+y[n−16]}+g ₆ {y[n−4]+y[n−12]}+g ₉ y[n−8]  (25.3)

C ₃ [n]=g ₃ {y[n]−y[n−16]}+g ₇ {y[n−4]−y[n−12]}  (25.4)

TABLE 4 g₀ (h₀ + h₃)/2 g₁ (h₀ − h₃)/2 g₂ (h₁ + h₂)/2 g₃ (h₁ − h₂)/2 g₄(h₄ + h₇)/2 g₅ (h₄ − h₇)/2 g₆ (h₅ + h₆)/2 g₇ (h₅ − h₆)/2 g₈ h₈ g₉ h₉

As for the example shown in FIG. 7, it can be seen from FIG. 8 that thenumber q of multiplier sections 52, 52′ is also equal to p+1=3, sinceL=5 is odd, according to equations (4) and (6) above, and that a set ofN=4 transformed signals C_(k)(n), with k=0,1,2,3, is generated throughoutput lines 60. According to equation (7) above, the further multipliersection 52′ also comprises a number s=2 of multipliers 54′ receiving theshifted signal Y(n−6) for combining thereof in parallel with acorresponding set of s=2 further transformed filter coefficients g₈ andg₉ derived from the coefficients of the linear phase prototype filter,as shown in Table 4. As for the example shown in FIG. 4, It can also beseen in FIG. 8 that while there are N=4 second adder sections 58, thereare t=N=4 third adders 59 since N=4 is even, according to equation (11)above.

I claim:
 1. A polyphase digital filter network based on a linear phaseprototype filter for use in a group demultiplexer for generating Noutput data signals associated with N channels from a correspondingFrequency Division Multiplexed input signal Y(n), said linear phaseprototype filter comprising N sub-filters being characterized by Lcoefficients forming NL coefficients for said prototype filter, saidpolyphase digital filter network comprising: L−1 Z^(−N) shift registersin series receiving said multiplexed input signal Y(n) to produce L−1corresponding shifted signals Y(n−rN), with r=1, . . . , L−1; a set of pfirst adder sections each receiving a distinct pair of signals from saidmultiplexed input signal Y(n) and said shifted signals Y(n−rN); a set ofq multiplier sections including p first multiplier sections each beingcoupled to a respective output of a corresponding one of said firstadder sections for combining each said output with a corresponding setof N transformed filter coefficients g_(i) derived from saidcoefficients of said linear phase prototype filter; said set of qmultiplier sections including a further multiplier section receivingshifted signal$Y( {n - {( \frac{L - 1}{2} )N}} )$

 where L is odd for combining thereof in parallel with a correspondingset of s further transformed filter coefficients g_(i) derived from thecoefficients of said linear phase prototype filter; a set of N secondadder sections each being coupled to distinct outputs of said multipliersections for producing a corresponding set of N transformed signalsC_(k)(n), with k=0, . . . , N−1; and a set of t third adders eachreceiving a distinct pair of signals {C_(T)(n),C_(T′)(n)} from saidtransformed signals C_(k)(n) for producing a first filtered signal A₀(n)and a set of N−1 filtered signals A_(k)(n+k), with k=1, . . . , N−1. 2.A polyphase digital filter network according to claim 1, wherein:$p = \{ {\begin{matrix}{L/2} & {{where}\quad L\quad {is}\quad {even}} \\\frac{L - 1}{2} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} $

said distinct pair of signals being defined by:{Y(n−mN),Y(n−(L−(1+m)N))} with: $m = \{ {\begin{matrix}{0,\ldots \quad,\frac{L - 2}{2}} & {{where}\quad L\quad {is}\quad {even}} \\{0,\ldots \quad,\frac{L - 3}{2}} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} $

and wherein: $q = \{ {\begin{matrix}p & {{where}\quad L\quad {is}\quad {even}} \\{p + 1} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};{s = \{ {\begin{matrix}{N/2} & {{where}\quad N\quad {is}\quad {even}} \\\frac{N + 1}{2} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2u}(n)},{C_{{2u} + 1}(n)}} \} \{ {\begin{matrix}{{{{for}\quad u} = 0},\ldots \quad,{{N/2} - 1}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = 0},\ldots \quad,\frac{N - 3}{2}} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2{({n - u - 1})}}(n)},{- {C_{{2{({n - u})}} - 1}(\quad n)}}} \} \quad \{ \quad {\begin{matrix}{{{{for}\quad u} = {N/2}},\ldots \quad,{N - 1}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = \frac{N + 1}{2}},\ldots \quad,{N - 1}} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix}\quad;{t = \{ {\begin{matrix}N & {{where}\quad N\quad {is}\quad {even}} \\{N - 1} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{{{and}{A_{u = \frac{N - 1}{2}}( {n + \frac{N - 1}{2}} )}} = {{C_{N - 1}(n)}\quad {where}\quad N\quad {is}\quad {{odd}.}}}} }} }}} }}} }} $


3. A polyphase digital filter network according to claim 1 or 2, furthercomprising: N−1 Z^(−k) shift registers receiving said filtered signalsA_(k)(n+k) to produce N−1 corresponding filtered signals A_(k)(n), withk=1, . . . , N−1.
 4. A polyphase digital filter network according toclaim 1 or 2, wherein each said first adder section comprises: a firstadder having a pair of positive inputs receiving said distinct pair ofsignals and an output; and a second adder having positive and invertinginputs receiving said distinct pair of signals respectively and anoutput; said first and second adder outputs forming said respectiveoutput of said corresponding first adder section.
 5. A polyphase digitalfilter network according to claim 4, wherein each said first multipliersection comprises N multipliers each having a respective output M_(i)and being coupled in parallel to said corresponding first adder outputfor combining thereof with N corresponding said transformed filtercoefficients g_(i) and s multipliers each having an output M_(i) andbeing coupled in parallel to said corresponding second adder sectionoutput for combining thereof with s corresponding said furthertransformed filter coefficients g_(i).
 6. A polyphase digital filternetwork according to claim 5, wherein said set of N transformed signalsC_(k)(n), with k=0,. . . , N−1, are produced by said set of N secondadder sections as follows:${{C_{k}(n)} = {\sum\limits_{i = {k + {Nl}}}M_{i}}};{{with}\{ {\begin{matrix}{{l = 0},\ldots \quad,{L/2}} & {{where}\quad L\quad {is}\quad {even}} \\{{l = 0},\ldots \quad,\frac{L - 1}{2}} & {{where}\quad L\quad {is}\quad {odd}\quad {and}\quad k\quad {is}\quad {even}} \\{{l = 0},\ldots \quad,\frac{L - 3}{2}} & {{where}\quad L\quad {is}\quad {odd}\quad {and}\quad k\quad {is}\quad {odd}}\end{matrix}.} }$


7. A polyphase/DFT digital group demultiplexer for generating N outputdata signals associated with N channels from a corresponding FrequencyDivision Multiplexed input signal Y(n), comprising: a polyphase digitalfilter network based on a linear phase prototype filter formed by Nsub-filters being characterized by L coefficients forming NLcoefficients for said prototype filter, said polyphase digital filternetwork comprising: L−1 Z^(−N) shift registers in series receiving saidmultiplexed input signal Y(n) to produce L−1 corresponding shiftedsignals Y(n−rN), with r=1, . . . , L−1; a set of p first adder sectionseach receiving a distinct pair of signals from said multiplexed inputsignal Y(n) and said shifted signals Y(n−rN); a set of q multipliersections including p first multiplier sections each being coupled to arespective output of a corresponding one of said first adder sectionsfor combining each said output with a corresponding set of N transformedfilter coefficients g_(i) derived from said coefficients of said linearphase prototype filter, wherein: said set of q multiplier sectionsincluding a further multiplier section receiving shifted signal$Y( {n - {( \frac{L - 1}{2} )N}} )$

 where L is odd for combining thereof with a corresponding set of sfurther transformed filter coefficients g_(i) derived from thecoefficients of said linear phase prototype filter; a set of N secondadder sections each being coupled to selected outputs of said multipliersections for producing a corresponding set of N transformed signalsC_(k), with k=0, . . . , N−1; a set of t third adders each receiving adistinct pair of signals {C_(T)(n),C_(T′)(n)} from said transformedsignals C_(k)(n) for producing a first filtered signal A₀(n) and a setof N−1 filtered signals A_(k)(n+k), with k=1, . . . , N−1; a set of N−1shift registers Z^(−k) receiving said filtered signals A_(k)(n+k) toproduce N−1 corresponding filtered signals A_(k)(n), with k=1, . . . ,N−1; a set of N phase offset multipliers receiving said filtered signalsA₀(n) and A_(k)(n) forming a set of filtered signals A_(k)(n), with k=0,. . . , N−1, for combining thereof with a corresponding set of N phaseoffset parameter w_(k), with k=0, . . . , N−1, to produce acorresponding set of phase offset filtered signals A*_(k)(n); DiscreteFourier Transform processor means for generating a set of N processedoutput signals B_(k)(n) from said corresponding set of phase offsetfiltered signals A*_(k)(n), with k=0, . . . , N−1; and a set of N outputalternate inverting multipliers each receiving a corresponding one ofsaid set of processed output signals B_(k)(n) to generate said N outputdata signals associated with said N channels.
 8. A polyphase/DFT digitalgroup demultiplexer according to claim 7 wherein:$p = \{ {\begin{matrix}{L/2} & {{where}\quad L\quad {is}\quad {even}} \\\frac{L - 1}{2} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} $

said distinct pair of signals being defined by:{Y(n−mN),Y(n−(L−(1+m)N))} with: $m = \{ {\begin{matrix}{0,\ldots \quad,\frac{L - 2}{2}} & {{where}\quad L\quad {is}\quad {even}} \\{0,\ldots \quad,\frac{L - 3}{2}} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} $

and wherein: $q = \{ {\begin{matrix}p & {{where}\quad L\quad {is}\quad {even}} \\{p + 1} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};{s = \{ {\begin{matrix}{N/2} & {{where}\quad N\quad {is}\quad {even}} \\\frac{N + 1}{2} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2u}(n)},{C_{{2u} + 1}(n)}} \} \{ {\begin{matrix}{{{{for}\quad u} = 0},\ldots \quad,{{N/2} - 1}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = 0},\ldots \quad,\frac{N - 3}{2}} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2{({n - u - 1})}}(n)},{- {C_{{2{({n - u})}} - 1}(\quad n)}}} \} \quad \{ \quad {\begin{matrix}{{{{for}\quad u} = {N/2}},\ldots \quad,{N - 1}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = \frac{N + 1}{2}},\ldots \quad,{N - 1}} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix}\quad;{t = \{ {\begin{matrix}N & {{where}\quad N\quad {is}\quad {even}} \\{N - 1} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{{{and}{A_{u = \frac{N - 1}{2}}( {n + \frac{N - 1}{2}} )}} = {{C_{N - 1}(n)}\quad {where}\quad N\quad {is}\quad {{odd}.}}}} }} }}} }}} }} $


9. A polyphase/DFT digital group demultiplexer according to claim 7 or8, wherein each said first adder section comprises: a first adder havinga pair of positive inputs receiving said distinct pair of signals and anoutput; and a second adder having positive and inverting inputsreceiving said distinct pair of signals respectively and an output; saidfirst and second adder outputs forming said respective output of saidcorresponding first adder section.
 10. A polyphase/DFT digital groupdemultiplexer according to claim 9, wherein each said first multipliersection comprises N multipliers M_(i) being coupled in parallel to saidcorresponding first adder output for combining thereof with Ncorresponding said transformed filter coefficients g_(i) and smultipliers M_(i) being coupled in parallel to said corresponding secondadder section output for combining thereof with s corresponding saidfurther transformed filter coefficients g_(i).
 11. A polyphase/DFTdigital group demultiplexer according to claim 10, wherein said set of Ntransformed signals C_(k)(n), with k=0, . . . , N−1, are produced bysaid set of N second adder sections as follows:${{C_{k}(n)} = {\sum\limits_{i = {k + {Nl}}}M_{i}}};{{with}\{ {\begin{matrix}{{l = 0},\ldots \quad,{L/2}} & {{where}\quad L\quad {is}\quad {even}} \\{{l = 0},\ldots \quad,\frac{L - 1}{2}} & {{where}\quad L\quad {is}\quad {odd}\quad {and}\quad k\quad {is}\quad {even}} \\{{l = 0},\ldots \quad,\frac{L - 3}{2}} & {{where}\quad L\quad {is}\quad {odd}\quad {and}\quad k\quad {is}\quad {odd}}\end{matrix}.} }$


12. A method of demultiplexing a Frequency Division Multiplexed inputsignal Y(n) for generating N output data signals associated with Nchannels, said method comprising the steps of: generating L−1 shiftedsignals Y(n−rN), with r=1, (l−1)N, from said multiplexed input signalY(n); coupling p pairs of distinct signals from said multiplexed inputsignal Y(n) and said shifted signals Y(n−rN) to produce p correspondingpairs of coupled output signals; combining each said pair of outputsignals with a corresponding set of N transformed filter coefficientsderived from coefficients of a linear phase prototype filter; combiningshifted signal$Y( {n - {( \frac{L - 1}{2} )N}} )$

 with a corresponding set of s further transformed filter coefficientsderived from the coefficients of said linear phase prototype filter,whenever L is odd; coupling the results of said combining steps toproduce N transformed signals C_(k), with k=0, . . . , N−1; couplingdistinct pair of signals {C_(T)(n),C_(T′)(n)} from said transformedsignals C_(k)(n) for producing a first filtered signal A₀(n) and a setof N−1 filtered signals; shifting said filtered signals A_(k)(n+k) toproduce N−1 corresponding filtered signals A_(k)(n), with k=1, . . . ,N−1; phase offsetting said filtered signals A₀(n) and A_(k)(n) forming aset of filtered signals A_(k)(n), to produce a corresponding set ofphase offset filtered signals A*_(k)(n); applying a Discrete FourierTransform on said phase offset filtered signals A*_(k)(n) to generate aset of N output signals B_(k)(n), with k=0, . . . , N−1; and alternatelyinverting said output signals B_(k)(n) to generate said N output datasignals associated with said N channels.
 13. A method of demultiplexinga Frequency Division Multiplexed input signal according to claim 12,wherein: $p = \{ {\begin{matrix}{L/2} & {{where}\quad L\quad {is}\quad {even}} \\\frac{L - 1}{2} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} $

said distinct pair of signals being defined by:{Y(n−mN),Y(n−(L−(1+m)N))} with: $m = \{ {\begin{matrix}{0,\ldots \quad,\frac{L - 2}{2}} & {{where}\quad L\quad {is}\quad {even}} \\{0,\ldots \quad,\frac{L - 3}{2}} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};} $

and wherein: $q = \{ {\begin{matrix}p & {{where}\quad L\quad {is}\quad {even}} \\{p + 1} & {{where}\quad L\quad {is}\quad {odd}}\end{matrix};{s = \{ {\begin{matrix}{N/2} & {{where}\quad N\quad {is}\quad {even}} \\\frac{N + 1}{2} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2u}(n)},{C_{{2u} + 1}(n)}} \} \{ {\begin{matrix}{{{{for}\quad u} = 0},\ldots \quad,{N/2^{- 1}}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = 0},\ldots \quad,\frac{N - 3}{2}} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{\{ {{C_{T}(n)},{C_{T^{\prime}}(n)}} \} = {\{ {{C_{2{({n - u - 1})}}(n)},{- {C_{{2{({n - u})}} - 1}(\quad n)}}} \} \quad \{ \quad {\begin{matrix}{{{{for}\quad u} = 0},\ldots \quad,{N/2^{- 1}}} & {{where}\quad N\quad {is}\quad {even}} \\{{{{for}\quad u} = 0},\ldots \quad,\frac{N - 3}{2}} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix}\quad;{t = \{ {\begin{matrix}N & {{where}\quad N\quad {is}\quad {even}} \\{N - 1} & {{where}\quad N\quad {is}\quad {odd}}\end{matrix};{{{and}{A_{u = \frac{N - 1}{2}}( {n + \frac{N - 1}{2}} )}} = {{C_{N - 1}(n)}\quad {where}\quad N\quad {is}\quad {{odd}.}}}} }} }}} }}} }} $